27 citations · 211 across the 28 of their papers we have counts for
29 papers · 1 filter
Geometry of wave damping on the torus
Kiril Datchev, Perry Kleinhenz, Antoine Prouff
Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these…
Exponential time-decay for a one dimensional wave equation with coefficients of bounded variation
Kiril Datchev, Jacob Shapiro
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Und…
Low energy scattering asymptotics for planar obstacles
T. J. Christiansen, K. Datchev
We compute low energy asymptotics for the resolvent of a planar obstacle, and deduce asymptotics for the corresponding scattering matrix, scattering phase, and exterior Dirichlet-t…
Newton polygons and resonances of multiple delta-potentials
Kiril Datchev, Jeremy L. Marzuola, Jared Wunsch
We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of -dependent delta-function potentials on . In the cases of two…
Propagation of singularities for the wave equation
Dean Baskin, Kiril Datchev
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
Semiclassical resolvent bounds for compactly supported radial potentials
Kiril Datchev, Jeffrey Galkowski, Jacob Shapiro
We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator in dimension , where ,…
On the interaction of metric trapping and a boundary
Kiril Datchev, Jason Metcalfe, Jacob Shapiro +1
By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as…
Resolvent estimates, wave decay, and resonance-free regions for star-shaped waveguides
T. J. Christiansen, K. Datchev
Using coordinates , we introduce the notion that an unbounded domain in is star shaped with respect to . For s…
Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
Kiril Datchev, Perry Kleinhenz
We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples…
Semiclassical Estimates for Scattering on the Real Line
Kiril Datchev, Jacob Shapiro
We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has…
Wave asymptotics for waveguides and manifolds with infinite cylindrical ends
T. J. Christiansen, K. Datchev
We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off reso…
Exponential lower resolvent bounds far away from trapped sets
Kiril Datchev, Long Jin
We give examples of semiclassical Schrödinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The…
Iterative reconstruction of the wavespeed for the wave equation with bounded frequency boundary data
Kiril Datchev, Maarten V. de Hoop
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded…
Resonances and lower resolvent bounds
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis.
Quantitative limiting absorption principle in the semiclassical limit
Kiril Datchev
We give an elementary proof of Burq's resolvent bounds for long range semiclassical Schroedinger operators. Globally, the resolvent norm grows exponentially in the inverse semiclas…
Nontrapping surfaces of revolution with long living resonances
Kiril R. Datchev, Daniel D. Kang, Andre P. Kessler
We study resonances of surfaces of revolution obtained by removing a disk from a cone and attaching a hyperbolic cusp in its place. These surfaces include ones with nontrapping geo…
Approximation and equidistribution of phase shifts: spherical symmetry
Kiril Datchev, Jesse Gell-Redman, Andrew Hassell +1
Consider a semiclassical Hamiltonian \begin{equation*} H_{V, h} := h^{2} Δ+ V - E \end{equation*} where is a semiclassical parameter, is the positive Laplacian on $\mat…
Resonance free regions for nontrapping manifolds with cusps
Kiril Datchev
We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation,…
Semiclassical resolvent estimates at trapped sets
Kiril Datchev, András Vasy
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-tra…
Fractal Weyl laws for asymptotically hyperbolic manifolds
Kiril Datchev, Semyon Dyatlov
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined b…
Extending cutoff resolvent estimates via propagation of singularities
Kiril Datchev
We use a gluing method developed in joint work with András Vasy to show that polynomially bounded cutoff resolvent estimates at the real axis imply, up to a constant factor, the sa…
Resonant uniqueness of radial semiclassical Schrodinger operators
Kiril Datchev, Hamid Hezari
We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical S…
Spectral uniqueness of radial semiclassical Schrodinger operators
Kiril Datchev, Hamid Hezari, Ivan Ventura
We prove that the spectrum of an n-dimensional semiclassical radial Schrödinger operator determines the potential within a large class of potentials for which we assume no symmetry…
Propagation through trapped sets and semiclassical resolvent estimates
Kiril Datchev, András Vasy
Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicha…